求limx→0(根号2-根号(1+cosx))/(sin3x)^2的极限求详解

网友回答

limx→0(√2-√(1+cosx))/(sin3x)^2=lim(1-cosx)/[(sin3x)^2(√2+√(1+cosx))]
=lim(1-(1-2sin^2(x/2)))/[(sin3x)^2(√2+√(1+cosx))]
=lim2sin^2(x/2)/[(sin3x)^2(√2+√(1+cosx))]
=lim2sin^2(x/2)*1/4/(x/2)^2/[(sin3x)^2*9/(3x)^2*(√2+√(1+cosx))]
=2*1/4/9/2√2=√2/72